Re: Log[Product[]] expansion to Sum[Log[]]?
- To: mathgroup at smc.vnet.net
- Subject: [mg9210] Re: [mg9160] Log[Product[]] expansion to Sum[Log[]]?
- From: Allan Hayes <hay at haystack.demon.co.uk>
- Date: Tue, 21 Oct 1997 02:03:24 -0400
- Sender: owner-wri-mathgroup at wolfram.com
Julian Stoev <stoev at SPAM-RE-MO-VER-usa.net> [mg9160] Log[Product[]] expansion to Sum[Log[]]? I want Log[Product[SomeFunction[k],{k,1,N}]] to be transformed to Sum[Log[SomeFunction[k]],{k,1,N}] Julian: Locally we can use PowerExpand[Log[Product[fn[k],{k,1,3}]]] Log[fn[1]]+Log[fn[2]]+Log[fn[3]] But this does not work on Log[Product[SomeFunction[k],{k,1,N}]] The following works automatically Unprotect[Log]; Log[Product[fn[k],{k,1,n}]] := Sum[Log[fn[k]],{k,1,n}]; Log[HoldPattern[Times[x__fn]]]:=Log/@ Plus[x]; Protect[Log]; Check: Log[Product[fn[k],{k,1,n}]] Sum[Log[fn[k]], {k, 1, n}] Log[fn[1] fn[2]] Log[fn[1]] + Log[fn[2]] Log[fn[1]] Log[fn[1]] Log[Times[]] 0 Allan Hayes hay at haystack.demon.co.uk http://www.haystack.demon.co.uk/training.html voice:+44 (0)116 2714198 fax: +44 (0)116 2718642 Leicester, UK